Question 100
we will designate by $Z_{(5)}$ a certain subset of the set $\mathbb{Q}$ of rational numbers. A rational belongs to $Z_{(5)}$ If and only if there are fractions belonging to this rational such that $5$ Do not be a divisor of your denominator. (for example, the rational number $13/10$ does not belong to $Z_{(5)}$, since the denominator of all the fractions equal to $13/10$ It is a multiple of $5$. Instead, the rational $75 / 10$ belonging to $Z_{(5)}$ as $75 / 10=15 / 12$). Reasoningly answering the following questions:
a) What algebraic structure (semigroup, group, etc.) has $Z_{(5)}$ regarding the sum?
b) And about the product?
c) is it $Z_{(5)}$ a sub-stop of $\mathbb{Q}$?
d) is it $Z_{(5)}$ a $Z_{(5)}$-Vector space?
a) What algebraic structure (semigroup, group, etc.) has $Z_{(5)}$ regarding the sum?
b) And about the product?
c) is it $Z_{(5)}$ a sub-stop of $\mathbb{Q}$?
d) is it $Z_{(5)}$ a $Z_{(5)}$-Vector space?